Issue 37

P.S. van Lieshout et al., Frattura ed Integrità Strutturale, 37 (2016) 173-192; DOI: 10.3221/IGF-ESIS.37.24 179 Different methods have been developed to determine the shear stress amplitude acting on a critical plane. In this comparative study the Minimum Circumscribed Circle method was used. This method has been described in [7, 31, 33].                        2 , 1 , 1 345 1 2 af af (6)       , 1 , 1 1  1 3 af af whereby Figure 3 : Representation of the counter clockwise rotations about the , Z N and ' Z axis, defined through three Euler angles , ,    (a) Relationship between the two spherical angles  and  with respect to the local coordinate system with axes uvw (b) ; Reproduced from [32]. Modified Wohler Curve Method The MWCM considers the normal and shear stress components acting on a particular critical plane whereby the orientation of the critical plane is determined by a Maximum Variance Method (MVM). This MVM is based on the experimental observation that fatigue damage shows proportionality with the variance of a random uniaxial load signal, both for Gaussian and non-Gaussian loadings [34]. Therefore, the critical plane corresponds to the material plane which coincides with the direction along which the variance of the resolved shear stress is maximum. The complexity of the stress state is then expressed by the stress amplitude ratio     Δ / Δ n which indicates the degree of non- proportionality. Hereby,  n is the normal stress acting perpendicular to the critical plane and  is the resolved shear stress acting on the critical plane. The MWCM presumes that fatigue damage is independent of the (nominal) load path as long as the stress ratio and shear stress range relative to the critical plane are the same. Therefore, a linear relationship is suggested for the construction of a modified load specific SN-curve [34]. Fig. 4 illustrates how this load specific SN-curve is constructed based on the tension and torsional fatigue curves. The equations that represent this linear relationship are given in Eq. 7 and 8.                   , Δ Δ  Δ  2 A A A A ref (7)            0 0 k k k k (8) The MVM describes the orientation of the critical plane using two polar angles  and  with respect to the local nab coordinate system of the critical plane. The angle  represents the angle between the normal to the critical plane and the Z-axis of the global reference coordinate system, while angle  represents the angle between the projection of the normal